If it can be corrected using a smooth 3-parameter spline, how hard can it be to estimate those parameters automatically/manually using exposure bracketing? What it the consequence of recording data at the non-linear region and doing nothing to invert it (is that not sort of what film cameras used to do?)

Anything that is "per camera", I would suspect also to (possibly) depend on temperature, exposure time, moon phase and what not?

Is this simply from the behaviour of a diode near saturation, or is it some more intricate physical thing?